I personally recommend the Remington 700 action, they make very high quality firearms and the M700 action has been proven time and time again since it was made, and has been used heavily and extensively for 50 years now by hunters, long range shooters, military, L.E., and many other shooters world wide.
I would recommend getting the Remington 700 SPS Tactical or SPS Varmint in .308, but I don't know about the .300 WIN MAG. If you don't mind having two of the same firearms in different calibers then I would recommend a Remington 700P for the .300 WIN MAG.
As far as either SPS Tactical or SPS Varmint, it's really a personal decision on which you would prefer. The SPS Tactical has a 20" barrel and a hogue over mold stock, where as the SPS Varmint has a 26" barrel and a synthetic stock. Also, the SPS Tactical only has one sling swivel stud in the front while the SPS Varmint has two. That gives a bit of an advantage to the SPS Varmint in my opinion since you can have both a sling and a bipod on it at the same time, and when hunting that is a big advantage to me personally. However, if you have the money to spend, I do recommend the SPS Tactical over the Varmint if you have the money to purchase a new stock, such as a HS Precision, or a Bell and Carlson. Also, just as a bit of a heads up, the SPS Varmint is absolutely not free floated, and the SPS Tactical is called free floated, however if you rest the fore end of the stock on a sand bag, bipod, or a fallen tree while hunting, then the stock will bend and touch the barrel since it is rather flexible. And since the SPS Varmint's stock is not free floated, I also recommend switching it out. Anyways, I hope some of this will be useful for you with your purchases. Sincerely- Ace762.